Optical system and device using the same

ABSTRACT

A viewing optical system for display devices or an image pickup optical system, which can be used with high efficiency at a plurality of wavelengths and enables bright images to be viewed with satisfactory color reproducibility and well-corrected aberrations. The optical system comprises a first prism, a second prism and a volume hologram element disposed between them and cemented to them. The hologram element comprises a first volume hologram optimized in such a way as to effect diffraction at least at a first wavelength and a second hologram optimized in such a way as to effect diffraction at a second wavelength different from the first wavelength. The first and second holograms are identical with each other in terms of the shape and spacing of interference fringes on their surfaces but different from each other in terms of the spacing and tilt of interference fringes in their hologram media.

This application claims benefit of Japanese Patent application No.2001-222961 filed in Japan Jul. 24, 2001, the contents of which areincorporated by this reference.

BACKGROUND OF THE INVENTION

The present invention relates generally to an optical system and devicesusing the same, and more particularly to an optical system such as aviewing or image pickup optical system that is used with an imagedisplay device or the like which may be mounted over the head or face ofan observer or added to cellar phones or easy-to-carry informationterminals.

For the purposes of allowing individuals to enjoy large-screen images,image display devices, especially head or face-mounted type imagedisplay devices are now under increasing development. There is also agrowing demand for providing large-screen viewing of image-wise orcharacter-wise data on cellar phones or portable information terminals.

For instance, U.S. Pat. No. 2,993,319 proposes a vehicle-mounted displaydevice using a reflection hologram element having functions similar tothose of a beam splitter capable of reflecting and diffracting onlylight having a specific range of angles of incidence and transmittinglight having other angles of incidence. As proposed and shown in thispatent publication, the angle selectivity of the reflection hologramelement is used to achieve the beam splitter function of guiding lightfrom a light source to an observer.

A viewing optical system comprising a combination of a reflectionhologram element formed on a spherical substrate in the air with areflection hologram element formed on a planar substrate in the air isproposed in U.S. Pat. No. 4,874,214. In this case, the reflectionhologram formed on the planar substrate makes use of angle selectivity,thereby achieving the beam splitter function.

The aforesaid U.S. Pat. No. 2,993,319 refers only to means for achievinga hologram beam splitter using the angle selectivity of a monochromatic(a single band: wavelength band) corresponding to the green wavelengthregion. For instance, this patent publication does not pay any attentionto the case where, for instance, a beam splitter harnessing the angleselectivity of a reflection hologram element is designed for light inseveral (e.g., red (R), green (G) and blue (B) or three-band light)bands.

That patent publication does not also say anything specific about theprofile, etc. of optical powers for achieving the beam splitter functionmaking use of the angle selectivity of a reflection hologram element.

The viewing optical system proposed in U.S. Pat. No. 4,874,214 comprisesa hologram element having a spherical shape. It is here noted that ahologram element has two powers, i.e., optical power due to ageometrical shape and optical power due to its diffraction effect. Forinstance, two powers of a hologram element formed on a substrate memberof spherical shape are now explained with reference to FIGS. 27(a) and27(b). The hologram element has power due to a difference in densitybetween interference fringes as represented by the pitch of a periodicalstructure within the hologram element as shown in FIG. 27(a), andoptical power due to its geometrical shape as shown in FIG. 27(b). Hereassume R is the radius of curvature of the hologram substrate. Then, theoptical power Φ of a conventional optical refracting lens, and aconventional reflector may be calculated from the following equations:

Φ=(n−1)(1/R) for a refracting system

Φ=2/R for a front surface mirror

Φ=2n/R for a back-surface mirror

Here Φ is the optical power due to the geometrical shape,

n is the refractive index of a medium, and

R is the radius of curvature of the hologram substrate.

It is thus understood that to obtain a certain quantity of optical powerby the geometrical shape, the radius of curvature, R, of theback-surface mirror should be gentler than that of the front surfacemirror by 1/n.

To put it another way, if the interior of the reflection hologramelement is filled up with a medium with a refractive index n, forinstance, a glass or plastic medium as is the case with a back-surfacemirror, it is then possible to obtain large optical power due togeometrical shape, even when the geometrical shape has a gentle radiusof curvature, R.

Thus, if an arrangement ensuring to generate large optical power at sucha gentle radius of curvature R is used for an optical system, it is thenpossible to reduce aberrations produced at this hologram surface.

In the viewing optical system of U.S. Pat. No. 4,874,214 wherein thespacing between the planar surface and the spherical surface is notfilled up with a glass or plastic medium, however, the geometrical shapemust be constructed with a smaller radius of curvature R so as to obtainthe required quantity of optical power by the geometrical configurationhaving a spherical shape.

When the geometrical shape is constructed with a smaller radius ofcurvature R, however, it is difficult to display satisfactory imagesbecause of increases in the aberrations produced at this reflectingsurface. For lack of any optical surface in an optical path between theimage plane and the aforesaid curved surface, it is difficult to makesatisfactory correction for distortion.

SUMMARY OF THE INVENTION

Having been accomplished with a view of solving such problems with theprior art as described above, the primary object of the presentinvention is to provide a viewing or image pickup optical system usedwith image display devices, which system can be used with highefficiency at a plurality of wavelengths, enables bright images to beobserved with high color reproducibility, is easy to assemble, resist toimpacts such as vibrations, light in weight and compact in size, andmakes it possible to observe images well corrected for aberrations, anddevices using the same.

According to the first aspect of the present invention, the aforesaidobject is achieved by the provision of an optical system that isdisposed between an image plane and an optical pupil and havinggenerally positive power, wherein:

said optical system comprises a first prism having a refractive index ofgreater than 1, a second prism having a refracting index of greater than1, and a volume hologram element disposed between said first prism andsaid second prism and cemented thereto, wherein:

said volume hologram element comprises a first volume hologram optimizedin such a way as to effect Bragg diffraction at least at a firstwavelength and a second volume hologram optimized in such a way as toeffect Bragg diffraction at a second wavelength different from saidfirst wavelength, and said volume hologram element is designed in such away that diffraction efficiency thereof reaches a maximum at a firstangle of incidence and a first angle of reflection and diffraction whichvary with the position of said volume hologram element at least at saidfirst wavelength and at a second angle of incidence and a second angleof reflection and diffraction which vary with the position of saidvolume hologram element at least at said second wavelength (it is herenoted that the volume hologram element includes an element obtained bymulti-exposing a single-layer volume hologram film to light including aplurality of wavelengths or a multilayer hologram element, and that thefirst and second wavelengths refer to two wavelengths in the RGBwavelength region or, for instance, two wavelengths R1 and R2 chosen outof the R wavelength region of the RGB wavelength region),

said first prism is located on said optical pupil side and said secondprism is located on said image plane side,

said second prism has at least one reflecting surface formed at asurface thereof different from a surface thereof having said volumehologram element,

a light beam, which propagates from said optical pupil to said imageplane in a forward or backward direction and includes at least a raycomponent of said first wavelength and at least a ray component of saidsecond wavelength, passes through said volume hologram element in orderfrom said first prism side to said second prism side, whereupon saidlight beam is reflected at said reflecting surface in said second prismand reflected and diffracted by said volume hologram element in saidsecond prism, and

said first volume hologram and said second volume hologram are identicalwith each other in terms of interference fringe shape and spacing on thesurfaces thereof but are difference from each other in terms ofinterference fringe spacing and tilt in hologram media.

Why the aforesaid arrangement is used in the present invention, and howit works is now explained.

The optical system of the present invention is disposed between theimage plane and the optical pupil, and has generally positive power. Forbackward ray tracing, a light beam passing from the optical pupil to theimage plane is selected, and for forward ray tracing, a light beampassing from the image plane to the optical pupil is selected. When alight beam is passed in the forward ray tracing direction while an imagedisplay element is located at the image plane and the pupil of the eyeof an observer is placed in the vicinity of the position of the opticalpupil, the optical system may be used as a viewing or eyepiece opticalsystem. When a light beam from a subject positioned in front of theoptical pupil is passed in the backward ray tracing direction while animage pickup element such as a silver salt film or CCD is located at theimage plane, the optical system may be used as an image pickup opticalsystem.

Disposed between the image plane and the optical pupil and havinggenerally positive power, the optical system of the present inventioncomprises a first prism having a refractive index of greater than 1, asecond prism having a refractive index of greater than 1 and a volumehologram element disposed between the first prism and the second prismand cemented thereto. The first prism is positioned on the optical pupilside. The second prism is positioned on the image plane side, and has atleast one reflecting surface formed at a surface thereof different fromthe surface thereof having the volume hologram element.

The volume hologram element may be a multi-recorded or multi-layeredhologram element. The volume hologram element comprises a first volumehologram optimized in such a way as to effect Bragg diffraction at leastat a first wavelength and a second volume hologram optimized in such away as to effect Bragg diffraction at a second wavelength different fromthe first wavelength, and should be designed in such a way that thediffraction efficiency reaches a maximum at a first angle of incidenceand a first angle of reflection and diffraction that vary with theposition of the volume hologram element at at least the first wavelengthand at a second angle of incidence and a second angle of reflection anddiffraction that vary with the position of the volume hologram elementat at least the second wavelength.

Such a volume hologram element, for instance, may include an elementformed by multi-exposure of a single-layer volume hologram film to aplurality of wavelengths (multi-recording) or a multilayer hologramelement formed by recording holograms of different wavelengths on aplurality of layers, one wavelength for one layer. The first and secondwavelengths are understood to refer to two wavelengths chosen from theRGB wavelength bands or two wavelengths R1 and R2 chosen from, forinstance, the R region in the RGB wavelength band.

The optical system of the present invention is designed in such a waythat a light beam, which propagates from the optical pupil to the imageplane in a forward or backward direction and includes at least a raycomponent of the first wavelength and at least a ray component of thesecond wavelength, passes through the volume hologram element in orderfrom the first prism side to the second prism side, whereupon the lightbeam is reflected at the reflecting surface in the second prism andreflected and diffracted by the volume hologram element in the secondprism.

Thus, the interior of the optical system is filled up with the glass,plastic or other materials for the first prism, second prism and volumehologram element, whereby the optical power due to the surface shape ofeach optically active surfaces can be increased with satisfactorycorrection for aberrations such as spherical aberrations and coma.

In the optical system of the present invention, the volume hologramelement is interposed between the first prism and the second prism, andcemented to both prisms.

If a volume hologram element is used as a beam splitter positioned atthe boundary between the first prism and the second prism for branchingan optical path, diffraction efficiency approximate to 100% can then beobtained upon reflection and diffraction with no substantialtransmission loss, so that bright image display and image pickup can beachieved with no light quantity losses. If two prisms, i.e., the firstprism on the optical pupil side and the second prism on the image planeside are integrated with a volume hologram element sandwiched betweenthem into a one-piece member, it is then possible to eliminate anyoptical axis misalignment due to the presence of an air spacing uponassembling or troublesome setting operation. It is thus possible toachieve a viewing or image pickup system that is easy to assemble andresistant to impacts such as vibrations.

If the volume hologram element is cemented to the first and secondprisms while it is sandwiched between them, it is then possible to makethe volume hologram element dust-proof. It is thus possible to preventenlarged observation of dust, etc. and transfer of them onto the imageplane without recourse to any separate dust-proof member, andpenetration of moisture from outside into the volume hologram element,which may otherwise cause the volume hologram to expand, resulting in achange of the peak wavelength of diffraction efficiency.

In the optical system of the present invention, the first volumehologram and the second volume hologram should be identical with eachother in terms of their surface interference shape and spacing butshould be different from each other in terms of the interference fringespacing and tilt in their hologram media.

Why that arrangement is critical for the present invention is nowexplained.

For a better understanding, here consider a volume hologram element 6which is made up of three volume hologram layers 6 _(R), 6 _(G) and 6_(B) stacked one upon another, as shown in FIG. 8(a). Then assume thatthe volume hologram 6 _(R) is optimized in such a way as to effect Braggdiffraction at a specific wavelength in the R wavelength region, thevolume hologram 6 _(G) is optimized in such a way as to effect Braggdiffraction at a specific wavelength in the G wavelength region, and thevolume hologram 6 _(B) is optimized in such a way as to effect Braggdiffraction at a specific wavelength in the B wavelength region.

A volume hologram has the property of having the maximum diffractionefficiency at an optimized wavelength in such a way that Braggdiffraction takes place. Even at other wavelengths, however, that volumehologram generally has a diffraction efficiency depending on a shiftfrom the optimized wavelength. Accordingly, when light having a specificwavelength in the B wavelength region, upon incidence on a specificposition A in the volume hologram element 6 at an angle of incidencei_(B) optimized at that position A, is diffracted by the volume hologram6 _(B) in the volume hologram 6 at an angle of diffraction r_(B) withthe maximum efficiency to produce diffracted light 21 _(B), the incidentlight 20 _(B) is slightly, if not largely, diffracted by other volumeholograms 6 _(R) and 6 _(G) to produce diffracted light 21 _(BR) and 21_(BG), as shown in FIG. 8(a). Then, the angles of diffraction r_(BR) andr_(BG) of diffracted light 21 _(BR) and 21 _(BG) having specificwavelengths in the B wavelength region are generally different from theangle of diffraction r_(B) due to the volume hologram 6 _(B). Thus, whenthe same wavelength (i.e., the specific wavelength in the B wavelengthregion) is diffracted by the volume hologram 6 in a plurality ofdifferent directions, the image-formation capability of an opticalsystem, which uses such a volume hologram element 6 as a beam splitterand to which the present invention is applied, becomes worse (leading tonot only chromatic aberrations but also monochromatic aberration).

To prevent any diffraction of light of one such wavelength in pluraldirections according to the present invention, the surfaces of thevolume holograms 6 _(R), 6 _(G) and 6 _(B) forming the volume hologramelement 6 should be constructed of interference fringes having the sameshape and spacing, so that the angles of diffraction r_(BR) and r_(BG)in FIG. 8(a) become the same as the angle of diffraction r_(B) and,hence, each of the diffracted light 21 _(BR) and 21 _(BG) is incoincidence with the diffracted light 21 _(B), as shown in FIG. 8(b).Consequently, incident light having any desired wavelength is diffractedwith a specific angle of diffraction at any desired position in thevolume hologram element 6; diffraction of light having any desiredwavelength in plural directions is prevented.

It is here understood that the angle of diffraction of light diffractedby a volume hologram is determined by the shape and spacing ofinterference fringes on its surface or if the volume holograms 6 _(R), 6_(G) and 6 _(B) forming the volume hologram 6 are identical with oneanother in terms of their surface interference fringe shape and spacing,the three volume holograms 6 _(R), 6 _(G) and 6 _(B) have the same angleof diffraction, as explained just below.

Consider a volume hologram sandwiched between isotropically uniformmedia, as shown in FIG. 9. A region I is defined by the isotropicallyuniform medium on the entrance side, a region II is defined by thevolume hologram and a region II is defined by the isotropically uniformmedium on the transmission side, with x- and z-axes determined as shown.

A diffraction grating recorded in a phase type volume hologram may begiven by

ε=ε_(II)+Δε·cos(K·r)  (11)

where eII is the average dielectric constant of the hologram, Δe is theamplitude of dielectric constant modulation of the hologram, r is aposition vector, and K is a grating vector that may be represented by

K=2π/Λ(sin φ, 0, cos φ)  (12)

Here Λ is a grating spacing (interference fringe spacing), and φ is theangle of K with the z-axis. It is noted that (sin φ, 0, cos φ)represents that the x component is sin φ, the y component is 0, and thez component is a vector of cos φ, as hereinafter applies.

With respect to S-polarized light, a wave equation in the hologram isgiven by

∇² E+k ² εE=0  (13)

Here E is an electric field, and k is the magnitude of a wave vector invacuum, given by

k=2π/λ

For reason of the periodicity of the grating (interference fringes),Floquet's theorem may hold; the electric field E in the hologram may begiven by

E=ΣS ₁(z)exp(−jσ₁ ·r)  (15)

i

σ_(i) =ρ−iK  (16)

where j is an imaginary unit, and ρ is the wave vector of referencelight (zero-order diffracted light), i is an integer tantamount to theorder of diffraction in the case of a hologram, S₁(z) is the amplitudeof an i-th order diffracted light, and σ_(i) is the wave vector of ani-th order diffracted light.

Alternatively, ρ may be represented by

ρ=2π/λ×{square root over ( )}ε_(II)(sin θ, 0, cos θ)  (17)

Here θ is the angle of incidence of reference light (zero-order light)in the hologram.

Regarding the i-th diffracted light emerging from the hologram, thehologram surface tangential component of the wave vector must bepreserved according to phase matching conditions, as given by thefollowing equation:

k _(Ii) ·x ₀=σ_(i) ·x ₀ =k _(IIIi) ·x ₀  (18)

Here k_(Ii) and k_(IIIi) are the wave vectors of the i-th orderdiffracted light upon reflection and transmission outside of thehologram, respectively, and x₀ is a unit vector in the x-axis direction.

From equations (12), (16) and (17), the second term of equation (18) is

σ_(i) ·x ₀=2π/λ×{square root over ( )}ε_(II)×sin θ−i2π/Λ×sin φ  (19)

Since the grating (interference fringes) spacing Λs is

Λs=Λ/sin φ  (20)

equation (19) may be rewritten as

σ_(i) ·x ₀=2π/λ×{square root over ( )}ε_(II)×sin θ−i2π/Λs  (21)

In region I formed of the isotropically uniform medium, the magnitude ofthe wave vector of diffracted light is represented by

|k _(I1)|=2π/λ×{square root over ( )}ε_(I)  (22)

Here ε_(I) is the dielectric constant of region I.

Therefore, the z-component of the wave vector of diffracted light inregion I is $\begin{matrix}\begin{matrix}{{k_{Ii} \cdot z_{0}} = \quad \left\{ {{k_{Ii}}^{2} - \left( {\sigma_{i} \cdot x_{0}} \right)^{2}} \right\}^{1/2}} \\{= \quad {{- {k_{Ii}}}\left\{ {1 - {{1/ɛ_{1}} \times \left( {{\left. \sqrt{}ɛ_{II} \right. \times \sin \quad \theta} - {i\quad {\lambda/\Lambda}\quad s}} \right)^{2}}} \right\}^{1/2}}}\end{matrix} & (23)\end{matrix}$

so that the wave vector in region I is given by $\begin{matrix}{k_{Ii} = {2{\pi/\lambda} \times \left. \sqrt{}ɛ_{I} \right. \times \left( {{{1/\left. \sqrt{}ɛ_{I} \right.} \times \left( {{\left. \sqrt{}ɛ_{II} \right. \times \sin \quad \theta} - {i\quad {\lambda/\Lambda}\quad s}} \right)},0,{- \left\{ {1 - {{1/ɛ_{I}} \times \left( {{\left. \sqrt{}ɛ_{II} \right. \times \sin \quad \theta} - {i\quad {\lambda/\Lambda}\quad s}} \right)^{2}}} \right\}^{1/2}}} \right)}} & (24)\end{matrix}$

Here z₀ is a unit vector in the z-axis direction.

The wave vector in region III, too, is likewise given by $\begin{matrix}{k_{IIIi} = {2{\pi/\lambda} \times \left. \sqrt{}ɛ_{III} \right. \times \left( {{{1/\left. \sqrt{}ɛ_{III} \right.} \times \left( {{\left. \sqrt{}ɛ_{II} \right. \times \sin \quad \theta} - {i\quad {\lambda/\Lambda}\quad s}} \right)},0,\left\{ {1 - {{1/ɛ_{III}} \times \left( {{\left. \sqrt{}ɛ_{II} \right. \times \sin \quad \theta} - {i\quad {\lambda/\Lambda}\quad s}} \right)^{2}}} \right\}^{1/2}} \right)}} & (25)\end{matrix}$

Equations (24) and (25) indicate that the wave vector of diffractedlight emerging from the phase type volume hologram is dependent on itssurface grating spacing rather than on the three-dimensional structureof the grating (interference fringes).

It is thus understood that as is the case with a thin hologram, thedirection of diffraction of light emerging from the phase type volumehologram is determined by the grating (interference fringes) spacing onits surface.

For P-polarized light, the wave equation in the hologram with respect toa magnetic field H is written as follows:

∇² H−(∇ε/ε×∇)H+k ² εH=0  (26)

If, as is the case with S-polarized light, Floquet's theorem is used,then the magnetic field H in the hologram may be represented as

H=ΣU ₁(z)exp(−jσ₁ ·r)  (27)

i

Here U₁(z) is the magnitude of an i-th diffracted light at the magneticfield.

For the P-polarized light, too, it is understood that as is the casewith the S-polarized light, an i-th diffracted light emerging from thehologram has a hologram surface tangent component of its wave vectorpreserved according to phase matching conditions, and wave vectors inregions I and III are the same as those given by equations (24) and(25), so that the direction of diffraction of light is determined by thegrating (interference fringes) spacing on the surface of the hologram.

For an amplitude type hologram, too, electromagnetic waves propagatingtherethrough may be described as in equations (15) and (27) according toFloquet's theorem.

Accordingly, the direction of diffraction of light is determined by thegrating (interference fringes) spacing on the hologram surface as is thecase with the phase type volume hologram.

It is thus found that as is the case with a thin hologram, the directionof diffraction of light by the volume hologram is determined by theinterference fringe spacing on the hologram surface rather than by thethree-dimensional structure of the grating (interference fringes).

It is here noted that the holograms are identical with one another interms of interference fringe shape and spacing includes not only thecase where they are identical with one another at the same place butalso cases where the tilts of interference fringes vary within the rangeof ±5°, preferably ±1°, and the spacing of interference fringes varywithin the range of ±5%, preferably ±1%.

With the optical system of the present invention wherein the interiorthereof is filled with a transparent medium having a refractive index ofgreater than 1, for instance, glass or plastic material, the opticalpower defined by the reflecting surface and the reflection hologramplane upon reflection can be ensured at an ever gentler radius ofcurvature, R. It is thus possible to reduce, or make satisfactorycorrection for, aberrations produced at each reflecting surface. Sincethe interior of the optical system is constructed of a transparentmedium having a refractive index of greater than 1, a refracting surfaceis positioned in front of the image plane, so that satisfactorycorrection of distortion can be made.

Preferably in the optical system of the present invention, the first andsecond prisms should be formed of the same type medium.

It is also preferable that the shape of the surface of the first prismto which the volume hologram element is cemented is substantially thesame as the shape of the surface of the second prism to which the volumehologram element is cemented.

It is here noted that the phrase “substantially the same” implies thatsurface shape differences within the margin of errors on production arepermissible.

Generally in the optical system of the present invention, the volumehologram element is a film type plane hologram. The surface of the firstprism that is one substrate to which the plane hologram element isapplied, and the surface of the second prism that is another substrateto which the plane hologram element is applied, should be in a planar orcylindrical form.

Here reference is made to specific embodiments of what arrangements thesurfaces of the first and second prisms are positioned in. Some exampleswill be given later. As viewed in order of a ray propagating from theoptical pupil to the image plane, the first prism should preferablycomprise, at least, a first entrance surface for entering a ray from theoptical pupil into the first prism and a first exit surface throughwhich the ray leaves the first prism with a first prism medium filledbetween them. The second prism should preferably comprise, at least, afirst entrance surface for entering the ray emerging from the firstprism into the second prism, a reflecting surface for reflecting the raywithin the second prism and a second exit surface through which the rayleaves the second prism, with a second prism medium filled between them.Preferably in the second prism, that reflecting surface should beconfigured in such a concave curved shape as to give positive power tothe ray on reflection.

It is then preferable that the first entrance surface of the first prismin the optical system of the present invention is configured in such acurved shape as to give power to the ray on transmission, and the secondexit surface of the second prism is configured in such a curved shape asto give power to the ray on transmission.

Preferably in the optical system of the present invention, a ghost lightremoval member for preventing the ghost light from striking on theeyeball of an observer should be provided on an optically inactivesurface of the first and second prisms other than the optically activesurfaces for transmitting and reflecting light rays.

When the second exit surface of the second prism is defined as the uppersurface, it is effective to provide such ghost light removal members onthe bottom and side of the optical member. The “optically activesurface” also includes areas outside of the effective ray diameter inthe second exit surface, outside of the effective ray diameter in thereflecting surface of the second prism, and outside of the effective raydiameter in the first entrance surface of the first prism. It is alsoeffective to provide such members at these areas.

Preferably in the optical system of the present invention, therotationally asymmetric curved shape of the first entrance surface hasan action on correction of rotationally asymmetric aberrations.

Preferably in the optical system of the present invention, therotationally asymmetric curved shape of the first entrance surface ofthe first prism is constructed of a free-form surface having only onesymmetric plane that should preferably be in coincidence with theturn-back plane (Y-Z plane) of the optical axis.

Preferably in the optical system of the present invention, the shape ofthe second exit surface of the second prism is a rotationally asymmetricfree-from shape.

Thus, if the transmitting surface (the second exit surface of the secondprism) is positioned at the front surface of an image display element(in the case of a viewing optical system with the image display elementdisposed at the image plane while a light beam propagates in thebackward direction from the optical pupil to the image plane) or animage pickup element (in the case of an image pickup optical system withthe image pickup element located at the image plane while a light beampropagates in the forward direction from the optical pupil to the imageplane), it is then possible to make satisfactory correction fordistortions. It is noted that while the front surface of this imagedisplay element or image pickup element may be constructed of arotationally symmetric shape, it is more preferable to have recourse toa free-form surface so as to correct decentration aberrations occurringwhen optically active surfaces are decentered for the purpose ofslimming down the optical system.

Preferably in the optical system of the present invention, therotationally asymmetric curved shape of the second exit surface of thesecond prism is constructed of a free-form surface having only onesymmetric plane that should preferably be in coincidence with theturn-back plane (Y-Z plane) of the optical axis.

In the present invention, while the surfaces forming the first prism andthe surfaces forming the second prism should preferably be constructedof rotationally asymmetric surfaces such as free-form surfaces for thepurpose of achieving an optical system having satisfactory telecentricproperties with well-corrected rotationally asymmetric distortions, itis understood that they may be constructed of rotationally symmetricsurfaces such as spherical, and aspheric surfaces or, alternatively,anamorphic surfaces.

Preferably in the optical system of the present invention, chromaticaberrations of magnification of both the rotationally symmetriccomponent and the rotationally asymmetric component are corrected byallowing the volume hologram element to reflect and diffract light rays.

Thus, correction of chromatic aberrations of magnification of both therotationally symmetric component and the rotationally asymmetriccomponent with the reflection volume hologram element ensures highcontrasts.

In order to take advantage of the angle selectivity of a reflectionvolume hologram element thereby achieving the beam splitter function, itis desired for the optical system of the present invention to satisfy atleast one of the following conditions (1) and (2):

−0.20<PX4/PX<0.50  (1)

−0.20<PY4/PY<0.30  (2)

Here assume that the direction of an axial chief ray passing through thecenter of the optical pupil is the Z-axis direction, the decentrationdirection of the optical system and optical surfaces is the Y-axisdirection and the direction perpendicular to the Y-axis and Z-axis isthe X-axis direction, and let δy indicate the angle of a ray leaving theoptical system with respect to an axial chief ray upon projected ontothe Y-Z plane with the proviso that said ray leaves the optical systemwhen a ray having a minute height, d, is entered from the optical pupilside into the Y-Z plane parallel with the axial chief ray, δy/d indicatethe power, PY, of the optical system in the Y-direction, δx indicate theangle of a ray leaving the optical system with respect to an axial chiefray upon projected onto a plane perpendicular to the Y-Z plane andincluding that axial chief ray with the proviso that said ray leaves theoptical system when a ray having a minute height, d, is entered from theoptical pupil side into the X-Z plane parallel with the axial chief ray,and δx/d indicate the power, PX, of the optical system in the Xdirection. Likewise, assume that PY4 and PX4 are the powers of thereflecting surface in the second prism forming part of the opticalsystem in the Y and X directions, respectively.

When the values of the aforesaid conditions (1) and (2) are less thanthe lower limits of −0.20, the optical power of the decenteredreflecting surface becomes too large in a negative direction to correctdecentration aberrations produced at that reflecting surface. There arealso large variations in the angle of incidence of light rays on thereflection hologram plane upon transmission, resulting in multiplediffraction. Consequently, it is difficult to display high-definitionimages or the volume hologram element fails to function as a beamsplitter.

When the values of the aforesaid conditions (1) and (2) are greater thanthe respective upper limits of 0.50 and 0.30, the optical power of thedecentered reflecting surface becomes too large in a negative directionto correct decentration aberrations produced at that reflecting surface.There are also large variations in the angle of incidence of light rayson the reflection hologram plane upon transmission, resulting inmultiple diffraction. Consequently, it is difficult to displayhigh-definition images or the volume hologram element fails to functionas a beam splitter.

More preferably, the optical system of the present invention shouldsatisfy at least one of the following conditions (1-1) and (2-1):

0.00<PX4/PX<0.35  (1-1)

−0.10<PY4/PY<0.20  (2-1)

The lower and upper limits to these conditions have the same meanings asdescribed above.

Even more preferably, the optical system of the present invention shouldsatisfy at least one of the following conditions (1-2) and (2-2):

0.15<PX4/PX<0.25  (1-2)

0.00<PY4/PY<0.10  (2-2)

The lower and upper limits to these conditions have the same meanings asdescribed above.

In Example 1 given later, the values of these conditions are as follows.

PX4/PX=0.190

PY4/PY=0.045

The optical system of the present invention may also be embodied as aviewing optical system comprising a two-dimensional image displayelement disposed at the image plane, so that an image on thetwo-dimensional image display element can be observed on an enlargedscale.

For instance, this embodiment may be a head-mounted type image displaydevice comprising a body portion built in as the viewing optical system,a support member for supporting said body portion over the head of anobserver in such a way that the optical pupil of the viewing opticalsystem is kept at the eyeball position of the observer, and a speakermember for transmitting sounds to the ear of the observer.

Alternatively, that body portion may comprise a viewing optical systemfor the right eye and a viewing optical system for the left eye, andthat speaker member may comprise speaker means for the right ear andspeaker means for the left ear. In this case, an earphone may be used asthat speaker member.

The optical system of the present invention may be applied not only toviewing systems but also to image pickup systems. An image pickup systemmay have an image pickup element disposed at the image plane, so thatobject light can be entered from the optical pupil side into the imagepickup system to pick up an object image.

It is here noted that the axial chief ray for a viewing optical systemis defined by backward tracing of a light ray passing through an opticalpupil center forming an exit pupil and arriving at the center of atwo-dimensional image display element, and the axial chief ray for animage pickup optical system is defined by forward tracing of a light raypassing through an optical pupil center forming an aperture stop andarriving at the center of an image pickup element. Then, the opticalaxis is defined by a straight line form of axial chief ray leaving thecenter of the exit pupil or aperture stop and intersecting as far as thefirst entrance surface of the first prism and the Z-axis is defined bythis optical axis. The Y-axis is defined by an axis perpendicular to theZ-axis and found in the decentered planes forming the first prism, andan axis perpendicular to the Z-axis and the Y-axis is defined as theX-axis. The center of the exit pupil or aperture stop is defined as theorigin of a coordinate system for the viewing or image pickup opticalsystem of the present invention. In the present invention, the surfacenumbers are given according to the backward ray tracing from the exitpupil toward the two-dimensional image display element or according tothe forward ray tracing from the aperture stop toward the image pickupelement. The direction of the axial chief ray propagating from the exitpupil to the two-dimensional image display element or from the aperturestop to the image display element is defined as the positive directionof the Z-axis, the direction of the Y-axis toward the two-dimensionalimage display element or toward the image pickup element as the positivedirection of the Y-axis, and the direction of the X-axis forming a righthand system with the Y-axis and Z-axis as the positive direction of theX-axis.

Here the free-form surface used herein is defined by the followingequation (a). It is noted that the Z-axis of this defining equationprovides the axis of the free-form surface. $\begin{matrix}{Z = {{c\quad {r^{2}/\left\lbrack {1 + \left. \sqrt{}\left\{ {1 - {\left( {1 + k} \right)c^{2}r^{2}}} \right\} \right.} \right\rbrack}} + {\sum\limits_{j = 2}^{\infty}{C_{j}X^{m}Y^{n}}}}} & (a)\end{matrix}$

In equation (a), the first term is a spherical term and the second termis a free-form surface term.

In the spherical term,

c is the curvature of the apex,

k is a conic constant (conical constant), and

r={square root over ( )}(X²+Y²)

The free-form term is${\underset{j = 2}{\overset{\infty}{Z}}C_{j}X^{m}Y^{n}} = {{C_{2}X} + {C_{3}Y} + {C_{4}X^{2}} + {C_{5}{XY}} + {C_{6}Y^{2}} + {C_{7}X^{3}} + {C_{8}X^{2}Y} + {C_{9}X\quad Y^{2}} + {C_{10}Y^{3}} + {C_{11}X^{4}} + {C_{12}X^{3}Y} + {C_{13}X^{2}Y^{2}} + {C_{14}X\quad Y^{3}} + {C_{15}Y^{4}} + {C_{16}X^{5}} + {C_{17}X^{4}Y} + {C_{18}X^{3}Y^{2}} + {C_{19}X^{2}Y^{3}} + {C_{20}X\quad Y^{4}} + {C_{21}Y^{5}} + {C_{22}X^{6}} + {C_{23}X^{5}Y} + {C_{24}X^{4}Y^{2}} + {C_{25}X^{3}Y^{3}} + {C_{26}X^{2}Y^{4}} + {C_{27}X\quad Y^{5}} + {C_{28}Y^{6}} + {C_{29}X^{7}} + {C_{30}X^{6}Y} + {C_{31}X^{5}Y^{2}} + {C_{32}X^{4}Y^{3}} + {C_{33}X^{3}Y^{4}} + {C_{34}X^{2}Y^{5}} + {C_{35}X\quad Y^{6}} + {C_{36}Y^{7}}}$

Here Cj (j is an integer of 2 or greater) is a coefficient with theproviso that j={(m+n)²+m+3n}/2+1 (m and n are each an integer of greaterthan 0).

In general, the aforesaid free-form surface has no symmetric surface atboth the X-Z plane and the Y-Z plane. However, by reducing all theodd-numbered terms for X to zero, that free-form surface can have onlyone symmetric surface parallel with the Y-Z plane. For instance, thismay be achieved by reducing to zero the coefficients for the terms C₂,C₅, C₇, C₉, C₁₂, C₁₄, C₁₆, C₁₈, C₂₀, C₂₃, C₂₅, C₂₇, C₂₉, C₃₁, C₃₃, C₃₅,. . . .

By reducing all the odd-numbered terms for Y to zero, the free-formsurface can have only one symmetric surface parallel with the X-Z plane.For instance, this may be achieved by reducing to zero the coefficientsfor the terms C₃, C₅, C₈, C₁₀, C₁₂, C₁₄, C₁₇, C₁₉, C₂₁, C₂₃, C₂₅, C₂₇,C₃₀, C₃₂, C₃₄, C₃₆, . . . .

By defining any one of the directions of the aforesaid symmetricalsurface as a symmetrical surface and setting decentration in thecorresponding direction, for instance, setting the direction of theoptical system with respect to a symmetrical surface parallel with theY-Z plane in the Y-axis direction and the direction of the opticalsystem with respect to a symmetrical surface parallel with the X-Z planein the X-axis direction, it is possible to make effective correction forrotationally asymmetric aberrations produced due to decentration while,at the same time, productivity is improved.

The aforesaid defining equation (a) is merely provided as an example.The present invention has the feature of using a rotationally asymmetricsurface having only one symmetric surface thereby correctingrotationally asymmetric aberrations produced due to decentration and, atthe same time, improving productivity. However, it is understood thatsimilar effects are obtainable even for any defining equations otherthan the aforesaid defining equation (a).

In the present invention, the reflecting surface provided at the secondprism may be formed in a free-form surface shape symmetrical withrespect to plane, which has only one symmetric plane.

The volume hologram (HOE) of the volume hologram element according tothe present invention is defined as follows. FIG. 11 is illustrative ofthe principle for giving a definition of HOE according to the presentinvention.

First of all, ray tracing of wavelength λ entering and leaving an HOEplane is given by the following equation (b), using an optical pathdifference function Φ₀ on the HOE plane as defined with respect to thereference wavelength λ₀=HWL.

n _(d) Q _(d) ×N=n _(i) Q _(i) ×N+m(λ/λ₀)∇Φ₀ ×N  (b)

Here N is the normal vector of the HOE plane, n_(i) (n_(d)) is therefractive index of the entrance (emergence) side, Q_(i) (Q_(d)) is theentrance (emergence) vector (in vector), and m=HOR is the order ofdiffraction of emergent light.

If the HOE is fabricated (defined) by interference of object light froma two-point light source for the reference wavelength λ₀, i.e., a lightsource of point P₁=(HX1, HY1, HZ1) as shown in FIG. 12 and referencelight from a light source of point P₂=(HX2, HY2, HZ2), then

Φ₀=Φ₀ ^(2P) =n ₂ ·s ₂ ·r ₂ −n ₁ ·s ₁ ·r ₁

where r₁ (r₂) is the distance (>0) from point P₁ (P₂) to givencoordinates P on the HOE plane, n₁ (n₂) is the refractive index of themedium on which the HOE is positioned at the time of fabrication(definition) and the point P₁ (P₂) is located, and s₁=HV1, and s₂=HV2 isa symbol for taking the direction of propagation of light intoconsideration. This symbol is REA=+1 in the case where the light sourceis a divergent (real point) light source, and VIR=−1 in the case wherethe light source is a convergent (virtual point) light source. Inconjunction with the definition of the HOE in lens data, it is notedthat the refractive index n₁ (n₂) of the medium on which the HOE isplaced at the time of fabrication (definition) is defined by therefractive index of the side of the medium contiguous to the HOE planein the lens data, on which the point P₁ (P₂) is found.

Generally, the reference light and object light used for HOE fabricationare not always limited to spherical waves.

In this case, the optical path difference functionΦ₀ for the HOE may beexpressed in terms of the following equation (c) with the additionthereto of an additive phase termΦ₀ ^(Poly) (an optical path differencefunction at the reference wavelength λ₀) represented by a polynominal.

Φ₀=Φ₀ ^(2P)+Φ₀ ^(Poly)  (c)

Here, the polynominal is $\begin{matrix}{\Phi_{0}^{Poly} = \quad {\sum\limits_{j}{H_{j} \cdot x^{m} \cdot y^{n}}}} \\{= \quad {{H_{1}x} + {H_{2}y} + {H_{3}x^{2}} + {H_{4}x\quad y} + {H_{5}y^{2}} +}} \\{\quad {{H_{6}x^{3}} + {H_{7}x^{2}y} + {H_{8}x\quad y^{2}} + {H_{9}y^{3}} + \ldots}}\end{matrix}$

In general, this may be defined by

j={(m+n)² +m+3n}/2

Here, H_(j) is the coefficient of each term.

For convenience of optical design, the HOE may be defined byrepresenting the optical path difference functionΦ₀ in terms of theadditive term alone, as in the case of

Φ₀=Φ₀ ^(Poly)

For instance, if light beams from the two-point light source P₁ (P₂) arein coincidence with each other, the componentΦ₀ ^(2P) of the opticalpath difference functionΦ₀ by interference is then reduced down to zero.This is tantamount to the case where the optical path differencefunction is substantially represented by the additive term alone.

All the aforesaid explanation of the HOE holds true for localcoordinates using the origin of the HOE as reference.

Exemplified below are the constructive parameters for the definition ofthe HOE.

Surface No. Radius of Curvature Surface Spacing Object Plnae ∞ ∞ 1 ∞(stop) 100 2 150 (HOE{circle around (1)}) −75 HOE{circle around (1)} HV1(s₁): REA (+1) HV2 (s₂): VIR (−1) HOR (m): 1 HX1 = 0 HY1 = −3.40 × 10⁹HZ1 = −3.40 × 10⁹ HX2 = 0 HY2 = 2.50 × 10 HZ2 = −7.04 × 10 HWL (λ₀) =544 H1 −1.39 × 10⁻²¹ H2 −8.57 × 10⁻⁵ H3 −1.50 × 10⁻⁴

In Example 1 given later, the hologram element is defined as composed ofonly one HOE{circle around (1)} layer that diffracts the red band lightwith its center at 630-nm wavelength in an angle selective manner.Regarding the HOE for the blue band light with its center at 470-nmwavelength and the HOE for the green band light with its center at535-nm wavelength, however, no optical path difference function isgiven. This is because the shape and spacing of interference fringes onthe surface of the hologram are the same as those of HOE{circle around(1)} for the red band light, and so is the optical path differencefunction Φ₀ represented by equation (c). It is here noted that thespacings and tilts of the interference fringes in the hologram medium ofeach HOE differ as a matter of course; the spacings and tilts of theinterference fringes in the hologram medium of each HOE at discrete sixpoints in the hologram plane are indicated to show three or the red,green and blue volume holograms.

Still other objects and advantages of the invention will in part beobvious and will in part be apparent from the specification.

The invention accordingly comprises the features of construction,combinations of elements, and arrangement of parts, which will beexemplified in the construction hereinafter set forth, and the scope ofthe invention will be indicated in the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a Y-Z sectional schematic illustrative of Example 1 of theoptical system of the present invention, including its optical axis.

FIG. 2 is an aberration diagram illustrative of an image distortion inExample 1.

FIG. 3 is an aberration diagram illustrative of transverse aberrationsin Example 1.

FIG. 4 is illustrative of the wavelength dependency of the angle ofincidence of the red band light, green band light, and blue band lighton high diffraction efficiency areas as evaluated at positions of thevolume hologram in Example 1, where the angle of incidence is i=50.6°and the angle of reflection and diffraction is r=50.7°.

FIG. 5 is illustrative of the wavelength dependency of the angle ofincidence of the red band light, green band light, and blue band lighton high diffraction efficiency areas as evaluated at positions of thevolume hologram in Example 1, where the angle of incidence is i=52.4°and the angle of reflection and diffraction is r=52.5°.

FIG. 6 is illustrative of the wavelength dependency of the angle ofincidence of the red band light, green band light, and blue band lighton high diffraction efficiency areas as evaluated at positions of thevolume hologram in Example 1, where the angle of incidence is i=54.6°and the angle of reflection and diffraction is r=54.7°.

FIG. 7 is illustrative of a simulation model for the diffractionefficiency of Example 1.

FIG. 8 is illustrative of the fundamental principles of the volumehologram element used in the present invention.

FIG. 9 is illustrative of the fact that the direction of diffraction oflight by a volume hologram is determined by the interference fringespacing on the surface of the hologram.

FIG. 10 is a vector diagram illustrative of relations between K, k_(R),k_(S), K_(z), K_(Rz) and K_(Sz) in the case where Bragg condition issatisfied.

FIG. 11 is a principle view for giving a definition of the HOE accordingto the present invention.

FIG. 12 is a Y-Z sectional schematic illustrative of a viewing opticalsystem constructed using a ghost light removal member, including itsoptical axis.

FIG. 13 is illustrative of why light that transmits the volume hologramwithout being diffracted has adverse influences in the form of ghostlight.

FIG. 14 is illustrative of a head-mounted goggles type image displaydevice using the observation optical system according to the presentinvention, which is mounted over the head of an observer.

FIG. 15 is a sectional view taken on a section of FIG. 14.

FIG. 16 is illustrative of a head-mounted monocle type image displaydevice using the observation optical system according to the presentinvention, which is mounted over the head of an observer.

FIG. 17 is a front perspective view illustrative of the outside shape ofan electronic camera to which the image pickup optical system andviewing optical system according to the present invention are applied.

FIG. 18 is a rear perspective view illustrative of the electronic cameraof FIG. 17.

FIG. 19 is a sectional view illustrative of one construction of theelectronic camera of FIG. 17.

FIG. 20 is a conceptual rendering illustrative of another electroniccamera to which the image pickup optical system and viewing opticalsystem according to the present invention are applied.

FIG. 21 is a conceptual rendering illustrative of an electronicendoscope to which the image pickup optical system and viewing opticalsystem according to the present invention are applied.

FIG. 22 is a front perspective view illustrative of an uncoveredpersonal computer in which the image pickup optical system of thepresent invention is built in as an objective optical system.

FIG. 23 is a sectional view illustrative of a phototaking optical systemin the personal computer.

FIG. 24 is a side view of the state shown in FIG. 22.

FIGS. 25(a), 25(b) and 25(c) are a front and a side view of a cellularphone in which the phototaking optical system of the present inventionis built in as an objective optical system, and a sectional view of thatphototaking optical system, respectively.

FIG. 26 is illustrative of one preferable construction of how the HOE islocated with respect to the prism forming part of the optical system ofthe present invention.

FIGS. 27(a) and 27(b) are a front and a side view illustrative of twopowers in the case where a hologram element is provided on a sphericalsubstrate member.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Example 1 of the optical system according to the present invention isnow explained.

The constructive parameters of Example 1 will be set forth later.Example 1 is directed to a viewing optical system. As shown in FIG. 1,an axial chief ray 2 is defined by a light ray leaving the center of anexit pupil 1 (the center position of rotation of the eyeball of anobserver) and arriving at the center of an LCD 5 provided as atwo-dimensional image display element through a first prism 3 and asecond prism 4. An optical axis is defined by a straight line form ofaxial chief ray 2 propagating as far as a surface 3 ₁ of the first prism3 on the exit pupil 1 side, and the Z-axis is defined by this opticalaxis. An axis perpendicular to the Z-axis and found in the decenteredplanes of the prism-forming surfaces is defined as the X-axis, and anaxis perpendicular to the optical axis and perpendicular to the Y-axisis defined as the Z-axis. The center of the exit pupil 1 is defined asthe origin of the coordinate system. The direction of the axial chiefray 2 propagating from the exit pupil 1 to LCD 5 is defined as thepositive direction of the Z-axis, the direction of the Y-axis towardLCD5 as the positive direction of the Y-axis, and the direction of theX-axis forming a right hand system with the Y-axis and Z-axis as thepositive direction of the X-axis.

In Example 1, the first prism 3 and second prism 4 are decentered in theaforesaid Y-Z plane, and only one symmetric plane for each rotationallyasymmetric surface of the first prism 3 and second prism 4 is given bythe Y-Z plane.

Given for a decentered surface are the amount of decentration of theapex of that surface from the center of the origin of the optical systemin the X, Y and Z-axis directions) and the angles (α, β, γ(°)) of tiltof the center axis (the Z axis in the following formula (a) for afree-form surface) with respect to the X axis, the Y axis, and the Zaxis, respectively. It is here noted that the positive α and β meancounterclockwise rotation with respect to the positive directions of therespective axes, and the positive γ means clockwise rotation withrespect to the positive direction of the Z axis. Regarding how to how toperform rotation α, β and γ around the center axis of the surface, it isnoted that the center axis of the surface and its XYZ orthogonalcoordinates are rotated counterclockwise around the X-axis by α, thecenter axis of the rotated surface is rotated counterclockwise around anew coordinate system by β, the once rotated coordinate system isrotated counterclockwise around the Y-axis by β, and the center axis ofthe twice rotated surface is rotated clockwise around the Z-axis of anew coordinate system by γ.

Regarding the optically active surfaces forming the optical system ofExample 1, when a specific surface and the subsequent surface form acoaxial optical system, a surface spacing is given. Besides, the radiiof curvature of spherical surfaces, the refractive indices of media andAbbe's numbers are given as usual.

The free-form surface used herein is of such a shape as defined by theaforesaid equation (a), and the Z-axis of that defining equation is theaxis of the free-form surface.

Among the defining equations for other free-form surfaces, there isZernike polynomial given by the following formula (d). The axis ofZernike polynomial is given by the Z-axis of the defining formula. Therotationally asymmetric surface is defined by polar coordinates for theheight of the Z-axis with respect to the X-Y plane provided that R isthe distance from the Z axis within the X-Y plane and A is the azimuthangle round the Z axis, as expressed by the angle of rotation measuredfrom the X-axis.

x=R×cos (A)

y=R×sin (A) $\begin{matrix}\begin{matrix}{Z = \quad {D_{2} + {D_{3}R\quad {\cos (A)}} + {D_{4}\quad R\quad {\sin (A)}} + {D_{5}R^{2}\quad \cos \quad \left( {2A} \right)} +}} \\{\quad {{D_{6}\left( {R^{2} - 1} \right)} + {D_{7}R^{2}\quad \sin \quad \left( {2A} \right)} + {D_{8}R^{3}\quad \cos \quad \left( {3A} \right)} +}} \\{\quad {{{D_{9}\left( {{3R^{3}} - {2R}} \right)}\quad \cos \quad (A)} + {{D_{10}\left( {{3R^{3}} - {2R}} \right)}\quad \sin \quad (A)} + {D_{11}R^{3}\quad \sin \quad \left( {3A} \right)} +}} \\{\quad {{D_{12}R^{4}\quad \cos \quad \left( {4A} \right)} + {{D_{13}\left( {{4R^{4}} - {3R^{2}}} \right)}\quad \cos \quad \left( {2A} \right)} +}} \\{\quad {{D_{14}\left( {{6R^{4}} - {6R^{2}} + 1} \right)} + {{D_{15}\left( {{4R^{4}} - {3R^{2}}} \right)}{\sin \left( {2A} \right)}} +}} \\{\quad {{D_{16}R^{4}\quad \sin \quad \left( {4A} \right)} + {D_{17}R^{5}\cos \quad \left( {5A} \right)} + {{D_{18}\left( {{5R^{5}} - {4R^{3}}} \right)}{\cos \left( {3A} \right)}} +}} \\{\quad {{{D_{19}\left( {{10R^{5}} - {12R^{3}} + {3R}} \right)}\quad \cos \quad (A)} +}} \\{\quad {{{D_{20}\left( {{10R^{5}} - {12R^{3}} + {3R}} \right)}\quad \sin \quad (A)} + {{D_{21}\left( {{5R^{5}} - {4R^{3}}} \right)}\sin \quad \left( {3A} \right)} +}} \\{\quad {{D_{22}R^{5}\sin \quad \left( {5A} \right)} + {D_{23}R^{6}\cos \quad \left( {6A} \right)} + {{D_{24}\left( {{6R^{6}} - {5R^{4}}} \right)}\cos \quad \left( {4A} \right)} +}} \\{\quad {{{D_{25}\left( {{15R^{6}} - {20R^{4}} + {6R^{2}}} \right)}\cos \quad \left( {2A} \right)} +}} \\{\quad {{D_{26}\left( {{20R^{6}} - {30R^{4}} + {12R^{2}} - 1} \right)} +}} \\{\quad {{{D_{27}\left( {{15R^{6}} - {20R^{4}} + {6R^{2}}} \right)}{\sin \left( {2A} \right)}} + {{D_{28}\left( {{6R^{6}} - {5R^{4}}} \right)}{\sin \left( {4A} \right)}} +}} \\{\quad {D_{29}R^{6}\sin \quad \left( {6A} \right)}}\end{matrix} & (d)\end{matrix}$

Here Dm (m is an integer of 2 or greater). It is noted that when thisfree-form surface is designed in the form of an optical system symmetricin the X-axis direction, D₄, D₅, D₆, D₁₀, D₁₁, D₁₂, D₁₃, D₁₄, D₂₀, D₂₁,D₂₂, . . . are used.

The shape of a rotationally asymmetric free-form may also be defined bythe following equation (e). The Z-axis of that defining equation (e)provides the axis of the rotationally asymmetric surface.

Z=Σ _(nΣ) _(m) C _(nm) X ^(n) Y ^(n−m)   (e)

Here Σ_(n) represents that n for Σ is in the range of 0 to k, and Σ_(m)represents that m for Σ is in the range of 0 to n.

In Example 1 of the present invention, the shape of the free-fromsurface is expressed in terms of the aforesaid equation (a). However, itis understood that similar actions and effects are obtainable even byuse of the aforesaid equations (d) and (e).

Example 1 is now specifically explained. In this example, the presentinvention is explained with reference to an image display device using aviewing optical system.

FIG. 1 is a Y-Z sectional schematic of a viewing optical systemaccording to Example 1 of the present invention.

The viewing optical system according to this example comprises an LCD 5that is a two-dimensional image display element for displaying an imageto be viewed by an observer and located on the image plane side, and aneyepiece optical member for guiding a viewing image formed by thetwo-dimensional image display element to an exit pupil 1 formed at theposition (pupil plane) of the eyeball of the observer for observingpurposes.

The eyepiece optical member comprises a first prism 3 and a second prism4. It is here noted that the surface numbers for the optical system arein principle given in order of ray tracing from the exit pupil 1 to LCD5 (backward ray tracing). The same holds true for the surfaces of thefirst and second prisms.

The first prism 3 comprises a first entrance surface 3 ₁ and a firstexit surface 3 ₂ with a transparent prism medium such as glass orplastics sandwiched between them.

The second prism 4 comprises a second entrance surface 4 ₁, a reflectingsurface 4 ₂ and a second exit surface 4 ₃ with a transparent prismmedium such as glass or plastics sandwiched between them.

The first prism 3 and the second prism 4 are integrated together while areflection volume hologram (HOE) 6 acting as a hologram element issandwiched between them.

It is here noted that both the first prism 3 and the second prism 4 areformed of the same prism medium, e.g., glass or plastics.

The second exit surface 4 ₃ of the second prism 4 is located on the LCD5 side and has an action of transmitting a light ray from an image underobservation and entering the light ray into the second prism 4. Thissurface is configured in such a free-form surface shape having only onesymmetric surface as to give power to that light ray upon transmission.

The reflecting surface 4 ₂ has an action of reflecting the light ray inthe second prism 4, and is configured in such a concave curved shape (afree-form surface in this example) as to give positive power to thelight ray upon reflection. The reflecting surface 4 ₂ is also providedthereon with a mirror coating.

The second entrance surface 4 ₁ is formed of a cylindrical surfacehaving a curvature in the X-axis direction but no curvature in theY-axis direction, and has an action of allowing the light ray to leavethe second prism 4.

The first exit surface 3 ₂ of the first prism 3 is located on the secondprism 4 side and has an action of transmitting the light ray emergingfrom the second prism 4 and entering the light ray into the first prism3. This surface is formed in substantially the same shape as that of thesecond entrance surface 4 ₁ of the second prism 4.

The first entrance surface 3 ₁ has an action of allowing the light rayto leave the first prism 3, and is formed in such a free-form surfaceshape having only one symmetric surface as to give power to the lightray upon transmission. This first entrance surface has also an action ofcorrecting at least one of asymmetrical coma and astigmatism produced atthe aforesaid eyepiece optical member.

Only one symmetrical surface of the first entrance surface 3 ₁ of thefirst prism 3, the reflecting surface 4 ₂ of the second prism 4, and thesecond exit surface 4 ₃ of the second prism 4, each defined by afree-form surface, is in coincidence with the turn-back plane of theoptical axis (Y-Z plane).

In the viewing optical system according to Example 1, red band light,green band light and blue band light emerging from LCD 5 are enteredinto the second prism 4 through the second exit surface 4 ₃, striking ona volume hologram 6 applied over the second entrance surface 4 ₁ atfirst, second and third angles of incidence, respectively. At this time,the incident red band light, green band light and blue band light arereflected and diffracted at the plane of the volume hologram 6 at first,second and third angles of reflection and diffraction withreflection/diffraction efficiencies of approximately 100%, propagatingtoward the reflecting surface 4 ₂. Upon reflected at the reflectingsurface 4 ₂, they are incident on the volume hologram 6 applied over thesecond entrance surface 4 ₁ at angles of incidences other than thefirst, second and third angles of incidence. Then, the angles ofincidence depart from the angle selectivity for diffraction efficiencyof the volume hologram 6 having high diffraction efficiency; the redband light, green band light, and blue band light leaves the secondprism 4 through the volume hologram 6. Following this, the light beamsare entered into the first prism 3 through the first exit surface 3 ₂ ofthe first prism 3, and guided to the exit pupil 1 side upon passingthrough the first entrance surface 3 ₁ and leaving the first prism 3.

While Example 1 of the present invention has been explained withreference to the viewing optical system, it is understood that if,instead of LCD 5, an image pickup element 13 is disposed at the imageplane of the viewing optical system and an aperture stop 14 for stoppingdown the brightness of a light beam from an object is disposed at theexit pupil 1, it is then possible to make up an image pickup opticalsystem.

In that case, the second exit surface 4 ₃ of the second prism 4functions as a surface through which the light ray leaves the secondprism 4, and the second entrance surface 4 ₁ acts as a surface forentering the light ray into the second prism 4. The first exit surface 3₂ of the first prism 3 functions as a surface through which the lightray leaves the first prism 3, and the first entrance surface 3 ₁ acts asa surface for entering a light ray emanating from an object andtransmitting through the aperture stop 14 into the first prism 3.

The volume hologram 6 is constructed by laminating three R, G and Blayers or triple recording. As already explained, the hologram layer forthe red band light with its center at 630-nm wavelength, the hologramlayer for the green band light with its center at 525-nm wavelength andthe hologram layer for the blue band light with its center at 470-nmwavelength are the same in terms of interference fringe shape andspacing on the surfaces of the holograms but differ in terms ofinterference fringe spacing and tilt in the medium of the holograms.

At an area where the volume hologram 6 is used as a beam splitter havingrecourse to a combined reflection/diffraction and transmission action ofthe hologram plane, the angle of the chief ray with respect to thenormal to the hologram plane is in the angle range of 50.6° to 54.6°upon reflection and diffraction. In this case, chromatic aberrationsproduced at other refracting surfaces 4 ₃ and 3 ₁ of the optical systemare canceled using the optical power of the volume hologram 6 that alsoacts as a diffraction element, so that chromatic aberrations ofmagnification of rotationally symmetric and asymmetric components can becorrected. The incident light ray emerges at an angle of diffractionsubstantially approximate to direction reflection. At an area where thevolume hologram 6 is used as a beam splitter having recourse to acombined reflection/diffraction and transmission action of the hologramplane, the angle of the chief ray with respect to the normal to thehologram plane is in the angle range of −16.2° to −18.2° upontransmission.

FIG. 7 is a model diagram for simulation of the diffraction efficiencyof this example. Assume that the volume hologram element 6 cemented intoa medium n1 has an average refractive index n, an amplitude ofrefractive index modulation Δn and a hologram thickness t. Then, at acertain coordinate position A of the volume hologram element 6, thelight ray to be reflected and diffracted enters at an angle of incidenceof i° and leaves at an angle of reflection and diffraction of r°, eachwith respect to the normal. At the coordinate position A of the volumehologram element 6, the light ray to be transmitted enters at an angleof incidence of s° with respect to the normal.

FIGS. 4-6 show the results of simulation of diffraction efficiency,which was carried out with the application of the following parametersto Kogelnik's coupled wave theory. Areas where the red band light, greenband light and blue band light are each diffracted at a diffractionefficiency of 10% or greater are indicated in black.

The medium is n1=1.52, the average refractive index is n=1.52, theamplitude of refractive index modulation is Δn=0.017, the thickness ist=25 μm, the angle of incidence is i=50.6°, the angle of reflection anddiffraction is r=50.7°, and the center wavelength of the band is 0.63 μmfor red, 0.525 μm for green, and 0.47 μm for blue.

According to Kogelnik's Coupled Wave theory (The Bell System TechnicalJournal, Vol. 48, No. 9, pp. 2909-2497 (Nov. 1969), the diffractionefficiency, η, of the reflection hologram element 6 is given by thefollowing equation (A) on condition that absorption by a medium isneglected.

η=1/[1+(1−ξ²/ν²)/sin h ²{{square root over ( )}(ν²−ξ²)}]  (A)

wherein ν and ξ are given by

ν=πtΔn/{1{square root over ( )}(cos θ_(R)·cos θ_(S))}

ξ=t/2×(k _(Rz) +K _(z) −k _(Sz))

Here:

t is the thickness of a photosensitive material,

λ is the wavelength in vacuum,

θ_(R) is the angle of incident light with respect to the vector of thenormal to the hologram plane,

θ_(S) is the angle of diffracted light with respect to the vector of thenormal to the hologram plane,

k_(Rz) is the component of the wave vector of incident light in thedirection of the normal to the hologram plane,

k_(Sz) is the component of the wave vector of diffracted light in thedirection of the normal to the hologram plane,

K_(z) is the component of a diffraction grating vector in the directionof the normal to the hologram plane,

Δn is the amplitude of the refractive index modulation of a hologrammedium, and

n is the average refractive index of the hologram medium.

Here the wave vector, k, of light is given by |k|=2πn/λ, and thediffraction grating vector, K, is a vector vertical to the interferencefringe plane of a volume hologram, as given by |k|=2πn/Λ where Λ is theperiod of the interference fringe (grating spacing). It is here notedthat FIG. 10 is a vector diagram illustrative of what relations arefound among K, k_(R), k_(S), K_(z), k_(Rz) and k_(Sz) when Braggcondition is satisfied.

At a position of the volume hologram 6 in Example 1 where reflection anddiffraction take place at the angle of incidence of i=50.6° in the anglerange of 50.6° to 54.6° at the hologram plane and the angle ofreflection and diffraction of r=50.7°, reentrance transmitted light isincident on the volume hologram 6 at −16.2°. From FIG. 4 it is seen thatthe reentrance transmitted light of 0.63 μm±20 μm wavelengths for red,of 0.525 μm±20 μm wavelengths for green and 0.47 μm±20 μm wavelengthsfor blue does not overlap the high-diffraction-efficiency area uponreentrance at an angle of incidence of −16.2°; that is, it istransmitted as such.

FIG. 5 is similar to FIG. 4, showing the results of simulation ofdiffraction efficiency at a position of the volume hologram 6 in Example1 where reflection and diffraction take place at the angle of incidenceof i=52.4° in the angle range of 50.6° to 54.6° at the hologram planeand the angle of reflection and diffraction of r=52.5°.

At a place of the volume hologram 6 in Example 1 where reflection anddiffraction take place at the angle of incidence of i=52.4° in the anglerange of 50.6° to 54.6° at the hologram plane and the angle ofreflection and diffraction of r=52.5°, reentrance transmitted light isincident on the volume hologram 6 at −18.7°. From FIG. 5 it is seen thatthe reentrance transmitted light of 0.63 μm+20 μm wavelengths for red,of 0.525 μm±20 μm wavelengths for green and 0.47 μm±20 μm wavelengthsfor blue does not overlap the high-diffraction-efficiency area uponreentrance at an angle of incidence of −18.7; that is, it is transmittedas such.

FIG. 6 is similar to FIG. 4, showing the results of simulation ofdiffraction efficiency at a position of the volume hologram 6 in Example1 where reflection and diffraction take place at the angle of incidenceof i=54.6° in the angle range of 50.6° to 54.6° at the hologram planeand the angle of reflection and diffraction of r=54.7°.

At a place of the volume hologram 6 in Example 1 where reflection anddiffraction take place at the angle of incidence of i=54.6° in the anglerange of 50.6° to 54.6° at the hologram plane and the angle ofreflection and diffraction of r=54.7°, reentrance transmitted light isincident on the volume hologram 6 at −18.2°. From FIG. 6 it is seen thatthe reentrance transmitted light of 0.63 μm±20 μm wavelengths for red,of 0.525 μm±20 μm wavelengths for green and 0.47 μm±20 μm wavelengthsfor blue does not overlap the high-diffraction-efficiency area uponreentrance at an angle of incidence of −18.2°; that is, it istransmitted as such.

In Example 1, the light beam from LCD5 or the light beam emerging froman object and passing through the aperture stop 14 transmits through thevolume hologram 6. If, as shown in FIGS. 4 to 6, the volume hologram 6is set in such a way that the red, green and blue transmitted lightbeams transmit through the high-diffraction-efficiency areas where thered band light, green band light and blue band light are each diffractedat a diffraction efficiency of 10% or greater, especially through anangle-of-incidence range in an area located on a shorter wavelength sidethan a region where the shortest wavelength blue band light isdiffracted with high diffraction efficiency, it is then possible toconcurrently reflect and diffract the red band light, green band lightand blue band light incident at the angle of reflection and diffractionwith high diffraction efficiencies, and concurrently transmit the redband light, green band light and blue band light incident at the angleof transmission with little or no diffraction. It is thus possible toachieve a hologram color beam slitter that can use light componentshaving a plurality of wavelengths with ever higher efficiencies andpresent bright displays with satisfactory color reproducibility and aviewing or image pickup optical system for image display devices usingsuch a hologram color beam splitter.

It is noted that the optical system of Example 1 has a focal length of21.2 mm, an eye relief of 28.00 mm, a pupil diameter of φ4 mm and aworking distance (WD) of 7.34 mm, and the image display element used hasa diagonal length of 0.55 inch, an aspect ratio of 4:3 and a size of8.448 mm×11.264 mm. The center diopter is −1.0D, and the viewing fieldangle is 30.0° for horizontal full-angle of view and 22.7° for verticalfull-angle of view.

Set out below are the numerical data on Example 1. It is noted, however,that “FFS” is an abbreviation of free-form surface, “CYL” anabbreviation of cylindrical surface, “HOE” an abbreviation of reflectionhologram plane, and “RE” an abbreviation of reflecting surface.Regarding the cylindrical surface, Rx and Ry stand for the radius ofcurvature of the surface in the X-axis direction and the radius ofcurvature of the surface in the Y-axis direction, respectively. It isfurther noted that Λ is the spacing between the periodical structures(interference fringes) of the refractive index distribution of thevolume hologram in the hologram medium, Λs is the spacing between theperiodical structures (interference fringes) of the refractive indexdistribution of the volume hologram at the surface of the hologrammedium, and θ is the angle of tilt of the periodical structures(interference fringes) of the refractive index distribution of thevolume hologram in the hologram medium with respect to the surface ofthe hologram medium.

EXAMPLE 1

Surface Radius of Surface Displacement Refractive Abbe's No. No.Curvature separation and tilt index Object ∞ −1000.00 plane 1 ∞ (Pupil)2 FFS{circle around (1)} (1) 1.5254  56.2 3 CYL{circle around (1)} (2)1.5254  56.2 4 FFS{circle around (2)} (RE) (3) 1.5254  56.2 5 CYL{circlearound (1)} (4) 1.5254  56.2 (HOE{circle around (1)}) 6 FFS{circlearound (3)} (5) Image ∞ (6) plane CYL{circle around (1)} Rx −128.44 Ry ∞FSS{circle around (1)} C₄ 6.4041 × 10⁻³ C₆ 2.4142 × 10⁻² C₈ −7.2555 ×10⁻⁶ C₁₀ 2.7801 × 10⁻⁴ C₁₁ 4.9418 × 10⁻⁶ C₁₃ 4.5544 × 10⁻⁶ C₁₅ 9.4384 ×10⁻⁶, C₁₇ −5.7579 × 10⁻⁷, C₁₉ 1.1416 × 10⁻⁶ C₂₁ 3.1265 × 10⁻⁷ FSS{circlearound (2)} C₄ −8.6139 × 10⁻³ C₆ −2.0278 × 10⁻³ C₈ 1.9774 × 10⁻⁵ C₁₀2.8876 × 10⁻⁵ C₁₁ 6.1298 × 10⁻⁷ C₁₃ −4.2136 × 10⁻⁷ C₁₅ 3.6073 × 10⁻⁶ C₁₇−1.4625 × 10⁻⁷, C₁₉ 3.6548 × 10⁻⁷ C₂₁ 2.7253 × 10⁻⁷ FSS{circle around(3)} C₄ 1.0827 × 10⁻³ C₆ −2.3537 × 10⁻² C₈ −5.3117 × 10⁻⁴ C₁₀ −9.1443 ×10⁻⁴ C₁₁ −3.6029 × 10⁻⁵ C₁₃ 3.3466 × 10⁻⁴ C₁₅ 1.7611 × 10⁻⁴, C₁₇ 3.5504× 10⁻⁶, C₁₉ −1.9995 × 10⁻⁵ C₂₁ −7.1100 × 10⁻⁶ HOE{circle around (1)} HV1REA HV2 REA HOR 1 HX1 0.0 HY1 0.0 HZ1 0.0 HX2 0.0 HY2 0.0 HZ2 0.0 HWL:630 nm H₂ 4.7061 × 10⁻³ H₃ −7.1036 × 10⁻⁴ H₅ −7.1539 × 10⁻⁴ H₇ −4.1424 ×10⁻⁵ H₉ −1.0636 × 10⁻⁵ H₁₀ −5.1882 × 10⁻⁶ H₁₂ −8.2388 × 10⁻⁷ H₁₄ 2.3705× 10⁻⁷ H₁₆ −2.2896 × 10⁻⁸ H₁₈ 9.3498 × 10⁻⁹ H₂₀ −9.7852 × 10⁻⁸ H₂₁2.6510 × 10⁻⁸ H₂₃ 5.2548 × 10⁻⁹ H₂₅ −5.8710 × 10⁻¹⁰ H₂₇ −3.7959 × 10⁻⁹Displacement and tilt (1) X 0.00 Y −0.96 Z 28.15 α 10.11 β 0.00 γ 0.00Displacement and tilt (2) X 0.00 Y 4.01 Z 31.31 α 20.09 β 0.00 γ 0.00Displacement and tilt (3) X 0.00 Y 0.55 Z 39.00 α −13.97 β 0.00 γ 0.00Displacement and tilt (4) X 0.00 Y 4.01 Z 31.31 α 20.09 β 0.00 γ 0.00Displacements and tilt (5) X 0.00 Y 14.11 Z 36.09 α 68.95 β 0.00 γ 0.00Displacement and tilt (6) X 0.00 Y 20.57 Z 36.32 α −111.29 β 0.00 γ 0.00Hologram Data on Hologram for Red (630-nm Wavelength) Band Light inHOE{circle around (1)} Ray Coordinates Angle of Incidence Angle ofEmergence (mm) (°) (°) Ray No. X Y X Y X Y 1 0.000 1.357 0.000 50.6080.000 −50.769 2 0.000 −8.268 0.000 52.659 0.000 −53.436 3 8.319 −8.47812.547 53.819 −13.487 −54.564 4 7.533 1.159 10.722 50.697 −11.716−50.823 5 6.822 9.892 11.376 49.642 −12.264 −48.546 6 0.000 10.418 0.00050.053 0.000 −48.830 Interference Fringes Ray No. Λ (μm) Λs (μm) θ (°) 10.340 229.736  0.0846 2 0.360 50.430 0.4084 3 0.374 41.257 0.5195 40.343 38.257 0.5137 5 0.331 21.645 0.8761 6 0.330 29.966 0.6313

Hologram Data on Hologram for Green (525-nm Wavelength) Band Light inHOE{circle around (1)} Ray Coordinates Angle of Incidence Angle ofEmergence (mm) (°) (°) Ray No. X Y X Y X Y 1 0.000 1.367 0.000 50.6250.000 −50.756 2 0.000 −8.240 0.000 52.740 0.000 −53.378 3 8.309 −8.45312.641 53.903 −13.415 −54.516 4 7.517 1.170 10.790 50.717 −11.605−50.820 5 6.806 9.857 11.424 49.589 −12.154 −48.695 6 0.000 10.379 0.00050.000 0.000 −49.003 Interference Fringes Ray No. Λ (μm) Λs (μm) θ (°) 10.282 226.683  0.7129 2 0.299 50.750 0.3376 3 0.311 40.994 0.4353 40.285 34.456 0.4246 5 0.275 21.738 0.7249 6 0.274 30.091 0.5255

Hologram Data on Hologram for Blue (470-nm Wavelength) Band Light inHOE{circle around (1)} Ray Coordinates Angle of Incidence Angle ofEmergence (mm) (°) (°) Ray No. X Y X Y X Y 1 0.000 1.373 0.000 50.6360.000 −50.754 2 0.000 −8.221 0.000 52.793 0.000 −53.369 3 8.302 −8.43712.703 53.957 −13.402 −54.510 4 7.507 1.177 10.834 50.730 −11.568−50.823 5 6.795 9.833 11.456 49.554 −12.113 −48.753 6 0.000 10.354 0.00049.965 0.000 −49.071 Interference Fringes Ray No. Λ (μm) Λs (μm) θ (°) 10.256 235.813  0.0622 2 0.712 51.093 0.3048 3 0.283 41.438 0.3918 40.259 38.802 0.3821 5 0.250 21.925 0.6522 6 0.249 30.055 0.4748

FIG. 2 is an aberration diagram indicative of image distortions inExample 1, and FIG. 3 is an aberration diagram indicative of transverseaberrations in Example 1. In the latter, the bracketed figureshorizontal field angles and vertical field angles and transverseaberrations thereat are indicated.

It is noted that why the interference fringe spacings Λs, on the surfaceof the hologram medium, of the hologram for the red band light, greenband light, and blue band light in the HOE{circle around (1)} in theaforesaid tables are not perfectly identical with one another is thatthe ray coordinates vary slightly for each wavelength due to chromaticaberrations. When the coordinates on the surface of the hologram mediumare identical with one another, the interference fringe spacings Λs, onthe surface of the hologram medium, of the hologram for the red bandlight, green band light, and blue band light are equal to one another.

In this connection, FIG. 12 is a Y-Z sectional view inclusive of theoptical axis of the optical system of the present invention, showingthat light transmitting the volume hologram 6 without diffraction takesthe form of ghost light producing unsatisfactory influences.

Even when a light beam is incident at a given angle of incidence on thevolume hologram 6 in the above-exemplified arrangement, light rays inthe given wavelength region are not subjected to 100% diffraction andreflection. In other words, only slight a portion of the light beam isnot diffracted and reflected, producing unnecessary transmitted light.

For instance, if that transmitted light strikes on the bottom 3 ₃ orside (vertical to the paper) of the eyepiece optical system shown inFIG. 13, then the reflected light may possibly be entered into theeyeball of the viewer in the form of ghost light.

To avoid this, an arrangement wherein the side or bottom 3 ₃ of thefirst prism 3 or the side of the second prism 4 is painted or otherwiseprovided with a black coating material capable of absorbing light or thelike to form a ghost light removal member is added to the arrangement ofFIG. 1, as shown in FIG. 12. It is then preferable that the ghost lightremoval member 15 is also provided at areas included in opticallyinactive surfaces (other than the optically active surfaces of the firstprism 3 and the second prism 4, at which light beams are transmitted orreflected) outside of the effective ray diameter within the second exitsurface 4 ₃ of the second prism 4, the effective ray diameter within thereflecting surface 4 ₂ of the second prism, and the effective raydiameter within the first entrance surface 3 ₁ of the first prism 3.

The aforesaid viewing optical system and image pickup optical system ofthe present invention may be used as a viewing system for viewing objectimages through an eyepiece lens or a phototaking system for formingobject images and receiving the object images at an image pickup elementsuch as a CCD or silver salt film for phototaking. For instance, thepresent invention may be applied to microscopes, head-mounted imagedisplay devices, endoscopes, projectors, silver salt cameras, digitalcameras, VRT cameras, information processors such as personal computersor cellular phones with built-in phototaking devices, as exemplifiedbelow.

As an example, FIG. 14 is illustrative of a head-mounted goggles typeimage display device, which is mounted over the head of a viewer, andFIG. 15 is a sectional view of that device. In this embodiment, theviewing optical system according to the present invention is used as aneyepiece optical system 100 comprising an image display element 5, asshown in FIG. 16. A pair of such eyepiece optical systems 100 aresupported at an interpupillary distance to make up a portable imagedisplay device 102 that enables images to be viewed with both eyes, forinstance, an installable or head-mounted type image display device.

More specifically in the image display device proper 102, a pair of suchviewing optical system as described above are used as eyepiece opticalsystems 100 and optical display elements 5, each comprising a liquidcrystal display element, are provided in association therewith. Theimage display device proper 102 is provided with a continuouslyextending temple frame 103, as shown in FIG. 14, thereby holding theimage display device proper 102 in front of the eyes of the viewer. Asshown in FIG. 15, a cover member 91 is interposed between the exit pupilof each eyepiece optical system 100 and the first entrance surface 3 ₁of the first prism. For this cover member 91, any one of aplane-parallel plate, a positive lens and a negative lens may be used.

Additionally, a speaker 104 is added to the temple frame 103 so thatstereophonic sound can be heard simultaneously with observation ofimages. Thus, the display device body 102 having the speaker 104 isconnected with a playback 104 such as a portable video cassette via animage/sound transmission cord 105, so that the viewer can enjoy imagesand sounds while holding this playback 106 at any desired position of abelt or the like, as shown in FIG. 14. In FIG. 14, reference numeral 107stands for a control portion on the playback 106, which portioncomprises a switch, a volume or the like. It is here noted that theimage display device body 102 has built-in electronic parts for image,sound and other processing.

It is noted that the cord 105 may be provided with a jack for insertioninto an existing video deck. In addition, the cord may be connected to atuner for reception of TV waves to watch the television or to a computerto receive computer graphics images, computer-generated message images,etc. To eliminate awkward cords, an antenna may be additionally attachedto the image display device proper for reception of signals from outsidevia waves.

Furthermore, the viewing optical system of the present invention may beapplied to a head-mounted monocle type image display device wherein aneyepiece optical system is disposed in front of either one of both eyes.FIG. 16 is illustrative of such a monocle type image display devicemounted over the head of a viewer (e.g., the left eye in thisembodiment). In this arrangement, a image display device body 102comprising a set of eyepiece optical system including an image displayelement 5 is mounted at a position of a front frame 108 in front of theassociated eye, and the front frame 108 is provided with a continuouslyextending frame 103, so that the display device body 102 can be held infront of each eye of a viewer. The arrangement is otherwise the same asin FIG. 14, and so is not explained.

FIGS. 17, 18 and 19 are conceptual illustrations of the objectiveoptical system of a finder portion in an electronic camera, in whichpart of the image pickup optical system according to the presentinvention is incorporated. FIG. 17 is a front perspective view of theoutside shape of an electronic camera 40, and FIG. 18 is a rearperspective view of the same. FIG. 19 is a sectional view of theconstruction of the electronic camera 40.

In this embodiment, the electronic camera 40 comprises a phototakingoptical system 41 including a phototaking optical path 42, a finderoptical system 43 including a finder optical path 44, a shutter button45, a flash 46, a liquid crystal monitor 47 and so on. As the shutterbutton 45 mounted on the upper portion of the camera 40 is pressed down,phototaking occurs through a phototaking objective optical system 48. Anobject image formed by the phototaking objective optical system 48 isformed on the image pickup plane 50 of a CCD 49 via a filter 51 such asan optical low-pass filter F or an infrared cut filter.

The object image received at CCD 49 is displayed as an electronic imageon the liquid crystal monitor 47 via processing means 52, which monitoris mounted on the back of the camera. This processing means 52 isconnected with recording means 61 in which the phototaken electronicimage may be recorded. It is here noted that the recording means 61 maybe provided separately from the processing means 52 or, alternatively,it may be constructed in such a way that images are electronicallyrecorded and written therein by means of floppy disks or the like. Thiscamera may also be constructed in the form of a silver salt camera usinga silver salt film in place of CCD 49.

Moreover, a finder objective optical system 53 is located on the finderoptical path 44. This finder objective optical system 53 comprises acover lens 54, a positive lens group 57 whose position is adjustable forfocusing in the optical axis direction, an aperture stop 14, a firstprism 3 and a second prism 4. The cover lens 54 used as a cover memberis a lens group having negative power, and functions to enlarge theangle of view. It is here noted that the second prism 4 is constructedas described in Example 1 of the present invention, and furthercomprises a reflecting surface 4 ₄ on an optical path from a hologram 6provided on a second entrance surface 4 ₁ to a second exit surface 4 ₃,which optical path is taken by diffracted and reflected light from thehologram 6. An object image formed by the finder objective optical path53 on an image formation plane is in turn formed on the field frame of aPorro prism 55 that is an image erecting member.

It is here noted that the field frame is disposed between the firstreflecting surface 56 ₁ and the second reflecting surface 56 ₂ of thePorro prism 55 to separate them, and comprises the first reflectingsurface 56 ₁ to the fourth reflecting surface 56 ₄. In the rear of thePorro prism 55 there is located an eyepiece optical system 59 forguiding an erected image into the eyeball E of an observer.

With the thus constructed digital camera 40, it is possible to achievehigh performance and cost reductions, because the finder objectiveoptical system 53 is constructed of a reduced number of optical members.In addition, the optical path through the objective optical system 53 isby itself turned back; there is an increase in the degree of freedom inlocating the optical path in the camera, which is favorable inconsideration of design.

While no reference has been made to the construction of the phototakingobjective optical system 48 in the arrangement of FIG. 19, it isunderstood that, instead of the refracting type coaxial optical system,any one of the image pickup optical systems comprising two such prisms 3and 4 as shown in Example 1 of the present invention may be used as thephototaking objective optical system 48.

It is also understood that the eyepiece optical system 59 may beconstructed using any one of the eyepiece optical members comprising twosuch prisms 3 and 4 as described in Example 1 of the present invention.

FIG. 20 is a conceptual illustration of an embodiment wherein the imagepickup optical system of the present invention is incorporated in theobjective optical system 48 of a phototaking portion in the electroniccamera 40 and the viewing optical system of the present invention isincorporated in the eyepiece optical system 59 in the electronic camera40. In this embodiment, the phototaking objective optical system 48disposed on a phototaking optical path 42 comprises a cover member 45comprising a positive lens and any one of the image pickup opticalsystems comprising two such prisms 3 and 4 as described in Example 1 ofthe present invention. A filter 51 such as a low-pass filter or infraredcut filter is interposed between the second prism 4 and a CCD 49. Anobject image formed by this phototaking objective optical system 48 isformed on the image pickup plane 50 of CCD 49. The object image receivedat this CCD 49 is displayed as an electronic image on a liquid crystaldisplay element (LCD) 60 via processing means 52. This processing means52 also controls recording means 61 for recording the electronic imagephototaken by CCD 49 as electronic information. The image displayed onLCD 60 is guided to the eyeball E of the viewer via an eyepiece opticalsystem 59.

This eyepiece optical system 59 is made up of decentered prism opticalsystems 3 and 4 in a form similar to that of such a viewing opticalsystem as set forth in Example 1 of the present invention and a coverlens 9 located on the exit pupil side thereof. In the back of LCD 60there is located a backlight 92 for illuminating LCD 60. It is notedthat this phototaking objective optical system 48 may further compriseother lenses (a negative and a positive lens) on the object or imageside of the two prisms 3 and 4.

With the thus constructed camera 40, it is possible to achieve highperformance and cost reductions because the phototaking objectiveoptical system 48, and the eyepiece optical system 59 can be composed ofa reduced number of optical members. In addition, the optical systemscan be generally arranged on the same plane, and so the thickness of thecamera 40 can be reduced in the direction to that plane.

While the positive lens is disposed as the cover member 64 for thephototaking objective optical system 48 in this example, it isunderstood that a negative lens or a plane-parallel plate may instead beused.

Such a cover member is not always necessary. For instance, the surfacelocated nearest to the object side of the image pickup optical system ofthe present invention may be used as a combined cover member. In thiscase, that surface located nearest to the object side is defined by thefirst entrance surface 3 ₁ of the first prism 3. However, it is notedthat the entrance surface 3 ₁ is decentered with respect to the opticalaxis, and so the location of this surface in front of the camera createsan illusion of a misalignment with the center of the camera 40 for theuser, as viewed from the subject side (as is the case with a generalcamera, the user is usually positioned in the direction vertical to theentrance surface), giving uncomfortableness to the user. Accordingly,when the surface of the image-formation optical system located nearestthe object side is decentered as in the present invention, it ispreferable to provide the cover member 65 (or the cover lens 54),because the user can phototake images in much the same way as inexisting cameras with no trouble as viewed from the subject side.

FIG. 21 is a conceptual rendering of an embodiment wherein the imagepickup optical system of the present invention is built in an objectiveoptical system 82 in the viewing arrangement of an electronic endoscope,and the viewing optical system of the present invention is incorporatedin an eyepiece optical system 87 of the viewing arrangement of theelectronic endoscope. The objective optical system 82 of the viewingsystem and the eyepiece optical system 87 used herein are eachsubstantially similar in construction as in Example 1. As shown in FIG.21(a), this electronic endoscope arrangement comprises an electronicendscope 71, a light source unit 72 for supplying illumination light, avideo processor 73 for performing signal processing corresponding to theelectronic endoscope 71, a monitor 74 for displaying image signalsproduced from the video processor 73, a VTR deck 75 and a video disk 76connected to the video processor 73 for recording image signals, etc., avideo printer 77 for printing out image signals in the form of imagesand a head-mounted image display device (HMD) 78 such as one shown inFIG. 14. A leading end 80 of an insert 79 of the electronic endscope 71and its eyepiece unit 81 are constructed as shown in FIG. 21(b).

A light beam leaving the light source unit 72 passes through a lightguide fiber bundle 88 to illuminate a site under observation via anillumination objective optical system 89. Light from this site underobservation passes through the cover member 85 and arrives at theviewing objective optical system 82 at which it is formed as an objectimage. Passing through a filter 83 such as a low-pass filter or infraredcut filter, this object image is formed on the image pickup plane of aCCD 84. Then, this object image is converted to image signals by CCD 84,which are in turn displayed directly on the monitor 74 via the videoprocessor 73 shown in FIG. 21(a) and recorded in the VTR deck 75 andvideo disk 76 or printed out by the video printer 77 in the form ofimages. The image is also displayed on an image display element 5 (FIG.15) of HMD 78 so that the wearer can view it. At the same time, theimage signals converted by CCD 84 is displayed as an electronic image ona liquid crystal display element (LCD) 86 of the eyepiece portion 81 viaimage signal transmission means 93. The displayed image is guided to theeyeball E of the observer via the eyepiece optical system comprising theviewing optical system of the present invention.

With the thus constructed endoscope composed of a reduced number ofoptical members, it is possible to achieve high performance and costreductions. In addition, the objective optical system 80 is positionedin the longitudinal direction of the endoscope, and so the aforesaideffect is achievable while the diameter of the endoscope is reduced.

FIGS. 22, 23 and 24 illustrate a personal computer that is oneembodiment of information processors in which the image pickup opticalsystem of the present invention is built.

FIG. 22 is a front perspective view of a personal computer or PC 300 inan uncovered state, FIG. 23 is a sectional view of a phototaking opticalsystem 303 in PC 300, and FIG. 24 is a side view of FIG. 22. As shown inFIGS. 22 to 24, PC 300 comprises a keyboard 301 for allowing an operatorto enter information therein from outside, information processing andrecording means (not illustrated), a monitor 302 for displaying theinformation to the operator, and a phototaking optical system 303 forphototaking an image of the operator per se and nearby images. Themonitor 302 used herein may be a transmission type liquid crystaldisplay illuminated from its back side by means of a backlight (notshown), a reflection type liquid crystal display designed to reflectlight from its front side for display purposes, a CRT display or thelike. As shown, the phototaking optical system 303 is built in the rightupper portion of the monitor 302; however, it may be located at anydesired position, for instance, around the monitor 302 or the keyboard301.

This phototaking optical system 303 comprises an objective opticalsystem 200 comprising the image pickup optical system of the presentinvention, a phototaking optical path 304 on which the system 200 islocated, and an image pickup chip 204 for receiving images. The membersare built in PC 300.

In this embodiment, an IR cut filter 203 is additionally applied ontothe image pickup chip 204 to form a one-piece image pickup unit 206 thatcan be mounted at the rear end of the lens barrel 201 of the objectiveoptical system 200 in one-touch snap operation. Thus, any centering orinter-surface adjustment for the objective optical system 200 and imagepickup chip 204 can be dispensed with, and so smooth assembly isachieved. Further, the lens barrel 201 is provided at the other end witha cover glass 202 for protection of the objective optical system 200.

An object image received at the image pickup chip 204 is entered intothe processing means of PC 300 via a terminal 205 and displayed as anelectronic image on the monitor 302. As an example, an image 305phototaken of the operator is shown in FIG. 22. The image 305 may bedisplayed on a personal computer on the other end of the line by way ofprocessing means and the Internet or a telephone.

FIG. 25 is illustrative of a convenient-to-carry cellular phone that isone exemplary information processor in which the image pickup opticalsystem of the present invention is built.

FIGS. 25(a) and 25(b) are a front view and a side view of a cellularphone 400, and FIG. 25(c) is a sectional view of a phototaking opticalsystem 405. As shown, the cellular phone 400 comprises a microphone 401through which the voice of an operator is entered as information, aspeaker 402 through which the voice of a person on the other end of thelike is produced, an input dial 403 through which the information isentered by the operator, a monitor 404 for displaying images phototakenof the operator per se, the person on the other end of the line and soon as well as information such as telephone numbers, a phototakingoptical system 405, an antenna 406 for transmission and reception ofradio waves for communications, and processing means (not shown) forprocessing image information, communications information, input signals,etc. Here a liquid crystal display is used for the monitor 404. How therespective devices are arranged is not particularly limited to thearrangement shown in FIG. 25. This phototaking optical system 405comprises an image pickup optical system 200 of the present inventionmounted on a phototaking optical path 407 and an image pickup chip 204for receiving images, which are built in the cellular phone 400.

In this embodiment, an IR cut filter 203 is additionally applied ontothe image pickup chip 204 to form a one-piece image pickup unit 206 thatcan be mounted at the rear end of the lens barrel 201 of the objectiveoptical system 200 in one-touch snap operation. Thus, any centering orinter-surface adjustment for the objective optical system 200 and imagepickup chip 204 can be dispensed with, and so smooth assembly isachieved. Further, the lens barrel 201 is provided at the other end witha cover glass 202 for protection of the objective optical system 200.

An object image received at the image pickup chip 204 is entered intoprocessing means (not shown) via a terminal 205, so that the image isdisplayed as an electronic image on the monitor 404 and/or a monitor onthe other end of the line. To transmit the image to the person on theother end, the signal processing means has a signal processing functionof converting information on the object image received at the imagepickup chip 204 to transmittable signals.

FIG. 26 is illustrative of one preferable arrangement wherein adiffraction element such as a volume hologram is mounted on a prismforming the optical system of the present invention. In FIG. 26,decentered prisms P1 and P2 are the second prism 4 and first prism 3included in the optical system of the present invention, respectively.Here assume that an image plane C (e.g., the display plane of the imagedisplay element 5 or the image pickup plane of the image pickup element13) is of such a rectangular shape as shown in FIG. 27. Then, it ispreferable for the formation of beautiful images that a symmetricalplane D for the 1-1st surface of the decentered prism P1 (the secondexit surface 4 ₃ of the second prism 4) or the 2-2nd surface of thedecentered prism P2 (the first entrance surface 3 ₁ of the second prism4), which is in the form of a free-form surface symmetrical with respectto plane, is parallel with at least one of four sides that form thisimage place C.

Furthermore, when the image plane C is configured in the form of asquare or rectangle having four internal angles of approximately 90°, itis preferable that the symmetrical plane D for the free-form surfacesymmetrical with respect to plane is parallel with two sides of theimage plane C, which sides are parallel with each other, and thesymmetrical plane D is brought in coincidence with the position at whichthe image plane C is symmetrical with respect to the horizontal orvertical. With this arrangement, the prism can be incorporated in theoptical system with high precision, and so the optical system iseffective for mass production.

When some or all of the 1-1st surface (the second exit surface 4 ₃ ofthe second prism 4), the 1-2nd surface (the second entrance surface 4 ₁of the second prism 4), the 1-3rd surface (the reflecting surface 4 ₂ ofthe second prism 4), the 2-1st surface (the first exit surface 3 ₂ ofthe first prism 3), the 2-2nd surface (the first entrance surface 3 ₁ ofthe first prism 3), etc. that are optical surfaces forming thedecentered prisms P1 and P2 are configured in the form of free-formsurfaces symmetrical with respect to plane, symmetrical planes for themshould preferably be disposed on the same plane D in view of both designand aberration performance. Then, the symmetrical plane D and the powerplane of the diffraction element 6 should have the same relations asexplained above.

While the optical system of the present invention and devices using thesame have been explained with reference to many embodiments, it isunderstood that the present invention is not limited to such embodimentsand so many modifications may be possible.

The two-dimensional image display element disposed at the image plane 5to form a two-dimensional image display element in the optical system ofthe present invention is not limited to LCDs. For instance, PDPs, DMDsand organic ELs may be used. One-dimensional images formed by aone-dimensional array of LCDs, PDPs, DMDs, organic ELs, LEDs or the likemay be displayed by scanning with galvanomirrors or polygonal mirrorsor, alternatively, images may be displayed by two-dimensional scanningof point light sources such as LEDs.

The volume hologram element used herein may be of the multilayer typewherein volume holograms recorded at various wavelengths are stacked oneupon another or the multiple recorded type wherein one layer of volumehologram recording medium is multi-exposed to a plurality ofwavelengths.

The image pickup element used comprises electrical receiving elementssuch as CCDs or photosensitive elements such as silver salt films.

Thus, the present invention provides a viewing or image pickup opticalsystem that is suitable for use with cellar phones, portable informationterminals and head-mounted virtual image viewing devices, can be usedwith high efficiency at a plurality of wavelengths, and is easy toassemble, resistant to impacts such as vibrations, light in weight andcompact in size with well corrected aberrations, and devices using thesame.

What we claim is:
 1. An optical system which is disposed between animage plane and an optical pupil and having generally positive power,wherein: said optical system comprises a first prism having a refractiveindex of greater than 1, a second prism having a refracting index ofgreater than 1, and a volume hologram element disposed between saidfirst prism and said second prism and cemented thereto, wherein: saidvolume hologram element comprises a first volume hologram optimized insuch a way as to effect Bragg diffraction at least at a first wavelengthand a second volume hologram optimized in such a way as to effect Braggdiffraction at a second wavelength different from said first wavelength,and said volume hologram element is designed in such a way thatdiffraction efficiency thereof reaches a maximum at a first angle ofincidence and a first angle of reflection and diffraction which varywith the position of said volume hologram element at at least said firstwavelength and at a second angle of incidence and a second angle ofreflection and diffraction which vary with the position of said volumehologram element at at least said second wavelength, said first prism islocated on said optical pupil side and said second prism is located onsaid image plane side, said second prism has at least one reflectingsurface formed at a surface thereof different from a surface thereofhaving said volume hologram element, a light beam, which propagates fromsaid optical pupil to said image plane in a forward or backwarddirection and includes at least a ray component of said first wavelengthand at least a ray component of said second wavelength, passes throughsaid volume hologram element in order from said first prism side to saidsecond prism side, whereupon said light beam is reflected at saidreflecting surface in said second prism and reflected and diffracted bysaid volume hologram element in said second prism, and said first volumehologram and said second volume hologram are identical with each otherin terms of interference fringe shape and spacing on the surfacesthereof but are different from each other in terms of interferencefringe spacing and tilt in hologram media.
 2. The optical systemaccording to claim 1, wherein said first prism and said second prism areconstructed of the same medium.
 3. The optical system according to claim1, wherein a surface of said first prism to which said volume hologramelement is cemented and a surface of said second prism to which saidvolume hologram element is cemented are configured in much the sameshape.
 4. The optical system according to claim 3, wherein a surface ofsaid first prism to which said volume hologram element is cemented and asurface of said second prism to which said volume hologram element iscemented are each configured in a planar or cylindrical shape.
 5. Theoptical system according to claim 1, wherein, in order of a raypropagating from said optical pupil to said image plane, said firstprism comprises, at least, a first entrance surface for entering the rayfrom said optical pupil into said first prism and a first exit surfacethrough which the ray leaves said first prism with a first prism mediumfilled between them, said second prism comprises, at least, a firstentrance surface for entering a ray emerging from said first prism intosaid second prism, a reflecting surface for reflecting the ray withinsaid second prism and a second exit surface through which the ray leavessaid second prism, with a second prism medium filled between them, andsaid reflecting surface in said second prism is configured in such aconcave curved shape as to give positive power to the ray on reflection.6. The optical system according to claim 5, wherein said first entrancesurface of said first prism is configured in such a curved shape as togive power to the ray on transmission, and said second exit surface ofsaid second prism is configured in such a curved shape as to give powerto the ray on transmission.
 7. The optical system according to clam 1,wherein a ghost light removal member for preventing ghost light fromstriking on the eyeball of an observer is provided on an opticallyinactive surface of said first and second prisms other than opticallyactive surfaces for transmitting and reflecting light rays.
 8. Theoptical system according to claim 1, wherein a first entrance surface ofsaid first prism is configured in a rotationally asymmetric curved shapehaving an action on correction of rotationally asymmetric aberrations.9. The optical system according to claim 8, wherein said rotationallyasymmetric curved shape is constructed of a free-form surface havingonly one symmetric plane that is in coincidence with a turn-back plane(Y-Z plane) of an optical axis.
 10. The optical system according toclaim 1, wherein a second exit surface of said second prism isconfigured in a rotationally asymmetric curved shape.
 11. The opticalsystem according to claim 10, wherein said rotationally asymmetriccurved shape is constructed of a free-form surface having only onesymmetric plane that is in coincidence with a turn-back plane (Y-Zplane) of an optical axis.
 12. The optical system according to claim 1,wherein chromatic aberrations of magnification of both a rotationallysymmetric component and a rotationally asymmetric component arecorrected by allowing said volume hologram element to reflect anddiffract the light ray.
 13. The optical system according to claim 1,wherein said reflecting surface of said second prism satisfies at leastone of the following conditions (1) and (2): −0.20<PX4/PX<0.50  (1)−0.20<PY4/PY<0.30  (2) with the proviso that the decentration directionof the optical system is a Y-axis direction, a direction perpendicularto a turn-back plane of an optical axis is an X-axis direction, PX isthe power of the optical system in the X-axis direction, PY is the powerof the optical system in the Y-axis direction, PX4 is the power of thereflecting surface of the second prism in the X-axis direction, and PY4is the power of the reflecting surface of the second prism in the Y-axisdirection.
 14. The optical system according to claim 1, wherein atwo-dimensional image display element is disposed on said image plane toconstruct a viewing optical system enabling an image on saidtwo-dimensional image display element to be viewed on an enlarged scalefrom said optical pupil side.
 15. A head-mounted image display devicecomprising a body portion in which an optical system as recited in claim14 is built as a viewing optical system, a support member for supportingsaid body portion over the head of an observer 30 that said opticalpupil of said viewing optical system is held at an eyeball position ofthe observer, and a speaker member for giving sounds to the ear of saidobserver.
 16. The head-mounted image display device according to claim15, wherein said body portion comprising a viewing optical system forthe right eye and a viewing optical system for the left eye, and saidspeaker member comprises speaker means for the right ear and speakermeans for the left ear.
 17. The head-mounted image display deviceaccording to claim 15, wherein said speaker member is constructed of anearphone.
 18. The optical system according to claim 1, which is an imagepickup optical system comprising an image pickup element disposed onsaid image plane so that object light is entered from said optical pupilside to pick up an object image.
 19. An image pickup device comprisingsaid image pickup optical system as recited in claim 18 and means forobserving an object image received at said image pickup element.